A one-dimensional model for the oxidative coupling of methane (OCM) over La2O3/CaO catalyst in fixed bed reactor has been developed. This model was tested for isothermal, adiabatic and non-isothermal operation modes. The parameters studied were methane to oxygen (CH4/O-2) ratio, temperature, space velocity, dilution effect of N-2 and H2O in the feed. High CH4/O-2 ratio favored the OCM reaction but gave low yield of ethylene due to insufficient oxygen under isothermal mode. Conversion, selectivity and yield increased with the temperature and a maximum value of yield was obtained at 1098 K. The presence of inert N-2 gas and H2O in feed gave positive effect to the yield in the process. Non-isothermal and adiabatic operations gave a temperature rise during OCM reaction which led to series of reactions that affected the system conversion, yield and selectivity of the desired product. Therefore, feed temperature, CH4/O-2 feed ratio and contact time are important parameters in order to control reactor run-away conditions.